LMFDB - Embedded newform 6014.2.a.l.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.181456 q^{3} +1.00000 q^{4} +3.41962 q^{5} +0.181456 q^{6} +3.19929 q^{7} -1.00000 q^{8} -2.96707 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.181456 q^{3} +1.00000 q^{4} +3.41962 q^{5} +0.181456 q^{6} +3.19929 q^{7} -1.00000 q^{8} -2.96707 q^{9} -3.41962 q^{10} -0.937697 q^{11} -0.181456 q^{12} +3.37036 q^{13} -3.19929 q^{14} -0.620509 q^{15} +1.00000 q^{16} +1.87326 q^{17} +2.96707 q^{18} +5.76224 q^{19} +3.41962 q^{20} -0.580530 q^{21} +0.937697 q^{22} +5.78440 q^{23} +0.181456 q^{24} +6.69378 q^{25} -3.37036 q^{26} +1.08276 q^{27} +3.19929 q^{28} +4.63956 q^{29} +0.620509 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.170150 q^{33} -1.87326 q^{34} +10.9404 q^{35} -2.96707 q^{36} +8.37299 q^{37} -5.76224 q^{38} -0.611571 q^{39} -3.41962 q^{40} -10.0201 q^{41} +0.580530 q^{42} +4.69437 q^{43} -0.937697 q^{44} -10.1463 q^{45} -5.78440 q^{46} -7.36262 q^{47} -0.181456 q^{48} +3.23547 q^{49} -6.69378 q^{50} -0.339913 q^{51} +3.37036 q^{52} -4.48353 q^{53} -1.08276 q^{54} -3.20656 q^{55} -3.19929 q^{56} -1.04559 q^{57} -4.63956 q^{58} -6.71310 q^{59} -0.620509 q^{60} -8.12603 q^{61} -1.00000 q^{62} -9.49254 q^{63} +1.00000 q^{64} +11.5253 q^{65} -0.170150 q^{66} +10.2716 q^{67} +1.87326 q^{68} -1.04961 q^{69} -10.9404 q^{70} -12.2263 q^{71} +2.96707 q^{72} +8.21597 q^{73} -8.37299 q^{74} -1.21463 q^{75} +5.76224 q^{76} -2.99997 q^{77} +0.611571 q^{78} -11.8922 q^{79} +3.41962 q^{80} +8.70475 q^{81} +10.0201 q^{82} +10.7355 q^{83} -0.580530 q^{84} +6.40582 q^{85} -4.69437 q^{86} -0.841874 q^{87} +0.937697 q^{88} +7.48122 q^{89} +10.1463 q^{90} +10.7828 q^{91} +5.78440 q^{92} -0.181456 q^{93} +7.36262 q^{94} +19.7047 q^{95} +0.181456 q^{96} -1.00000 q^{97} -3.23547 q^{98} +2.78222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.181456	−0.104763	−0.0523817	−	0.998627i	$-0.516681\pi$
$3$	−0.181456	−0.104763	−0.0523817	+	0.998627i	$0.516681\pi$
$4$	1.00000	0.500000
$5$	3.41962	1.52930	0.764650	−	0.644446i	$-0.222912\pi$
$5$	3.41962	1.52930	0.764650	+	0.644446i	$0.222912\pi$
$6$	0.181456	0.0740790
$7$	3.19929	1.20922	0.604610	−	0.796522i	$-0.293329\pi$
$7$	3.19929	1.20922	0.604610	+	0.796522i	$0.293329\pi$
$8$	−1.00000	−0.353553
$9$	−2.96707	−0.989025
$10$	−3.41962	−1.08138
$11$	−0.937697	−0.282726	−0.141363	−	0.989958i	$-0.545149\pi$
$11$	−0.937697	−0.282726	−0.141363	+	0.989958i	$0.545149\pi$
$12$	−0.181456	−0.0523817
$13$	3.37036	0.934769	0.467384	−	0.884054i	$-0.345196\pi$
$13$	3.37036	0.934769	0.467384	+	0.884054i	$0.345196\pi$
$14$	−3.19929	−0.855047
$15$	−0.620509	−0.160215
$16$	1.00000	0.250000
$17$	1.87326	0.454332	0.227166	−	0.973856i	$-0.427054\pi$
$17$	1.87326	0.454332	0.227166	+	0.973856i	$0.427054\pi$
$18$	2.96707	0.699346
$19$	5.76224	1.32195	0.660974	−	0.750409i	$-0.270143\pi$
$19$	5.76224	1.32195	0.660974	+	0.750409i	$0.270143\pi$
$20$	3.41962	0.764650
$21$	−0.580530	−0.126682
$22$	0.937697	0.199918
$23$	5.78440	1.20613	0.603065	−	0.797692i	$-0.293946\pi$
$23$	5.78440	1.20613	0.603065	+	0.797692i	$0.293946\pi$
$24$	0.181456	0.0370395
$25$	6.69378	1.33876
$26$	−3.37036	−0.660981
$27$	1.08276	0.208377
$28$	3.19929	0.604610
$29$	4.63956	0.861544	0.430772	−	0.902461i	$-0.358241\pi$
$29$	4.63956	0.861544	0.430772	+	0.902461i	$0.358241\pi$
$30$	0.620509	0.113289
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	0.170150	0.0296194
$34$	−1.87326	−0.321261
$35$	10.9404	1.84926
$36$	−2.96707	−0.494512
$37$	8.37299	1.37651	0.688255	−	0.725468i	$-0.258377\pi$
$37$	8.37299	1.37651	0.688255	+	0.725468i	$0.258377\pi$
$38$	−5.76224	−0.934759
$39$	−0.611571	−0.0979297
$40$	−3.41962	−0.540689
$41$	−10.0201	−1.56488	−0.782439	−	0.622727i	$-0.786025\pi$
$41$	−10.0201	−1.56488	−0.782439	+	0.622727i	$0.786025\pi$
$42$	0.580530	0.0895777
$43$	4.69437	0.715885	0.357942	−	0.933744i	$-0.383478\pi$
$43$	4.69437	0.715885	0.357942	+	0.933744i	$0.383478\pi$
$44$	−0.937697	−0.141363
$45$	−10.1463	−1.51251
$46$	−5.78440	−0.852863
$47$	−7.36262	−1.07395	−0.536975	−	0.843598i	$-0.680433\pi$
$47$	−7.36262	−1.07395	−0.536975	+	0.843598i	$0.680433\pi$
$48$	−0.181456	−0.0261909
$49$	3.23547	0.462211
$50$	−6.69378	−0.946644
$51$	−0.339913	−0.0475974
$52$	3.37036	0.467384
$53$	−4.48353	−0.615860	−0.307930	−	0.951409i	$-0.599636\pi$
$53$	−4.48353	−0.615860	−0.307930	+	0.951409i	$0.599636\pi$
$54$	−1.08276	−0.147345
$55$	−3.20656	−0.432373
$56$	−3.19929	−0.427523
$57$	−1.04559	−0.138492
$58$	−4.63956	−0.609204
$59$	−6.71310	−0.873972	−0.436986	−	0.899468i	$-0.643954\pi$
$59$	−6.71310	−0.873972	−0.436986	+	0.899468i	$0.643954\pi$
$60$	−0.620509	−0.0801074
$61$	−8.12603	−1.04043	−0.520216	−	0.854035i	$-0.674149\pi$
$61$	−8.12603	−1.04043	−0.520216	+	0.854035i	$0.674149\pi$
$62$	−1.00000	−0.127000
$63$	−9.49254	−1.19595
$64$	1.00000	0.125000
$65$	11.5253	1.42954
$66$	−0.170150	−0.0209441
$67$	10.2716	1.25488	0.627438	−	0.778666i	$-0.284104\pi$
$67$	10.2716	1.25488	0.627438	+	0.778666i	$0.284104\pi$
$68$	1.87326	0.227166
$69$	−1.04961	−0.126358
$70$	−10.9404	−1.30762
$71$	−12.2263	−1.45100	−0.725498	−	0.688224i	$-0.758391\pi$
$71$	−12.2263	−1.45100	−0.725498	+	0.688224i	$0.758391\pi$
$72$	2.96707	0.349673
$73$	8.21597	0.961607	0.480804	−	0.876828i	$-0.340345\pi$
$73$	8.21597	0.961607	0.480804	+	0.876828i	$0.340345\pi$
$74$	−8.37299	−0.973340
$75$	−1.21463	−0.140253
$76$	5.76224	0.660974
$77$	−2.99997	−0.341878
$78$	0.611571	0.0692467
$79$	−11.8922	−1.33798	−0.668989	−	0.743272i	$-0.733273\pi$
$79$	−11.8922	−1.33798	−0.668989	+	0.743272i	$0.733273\pi$
$80$	3.41962	0.382325
$81$	8.70475	0.967194
$82$	10.0201	1.10654
$83$	10.7355	1.17838	0.589189	−	0.807995i	$-0.299447\pi$
$83$	10.7355	1.17838	0.589189	+	0.807995i	$0.299447\pi$
$84$	−0.580530	−0.0633410
$85$	6.40582	0.694809
$86$	−4.69437	−0.506207
$87$	−0.841874	−0.0902584
$88$	0.937697	0.0999588
$89$	7.48122	0.793007	0.396504	−	0.918033i	$-0.370223\pi$
$89$	7.48122	0.793007	0.396504	+	0.918033i	$0.370223\pi$
$90$	10.1463	1.06951
$91$	10.7828	1.13034
$92$	5.78440	0.603065
$93$	−0.181456	−0.0188161
$94$	7.36262	0.759397
$95$	19.7047	2.02165
$96$	0.181456	0.0185197
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−3.23547	−0.326832
$99$	2.78222	0.279623
$100$	6.69378	0.669378
$101$	−0.582823	−0.0579930	−0.0289965	−	0.999580i	$-0.509231\pi$
$101$	−0.582823	−0.0579930	−0.0289965	+	0.999580i	$0.509231\pi$
$102$	0.339913	0.0336564
$103$	−5.66535	−0.558224	−0.279112	−	0.960259i	$-0.590040\pi$
$103$	−5.66535	−0.558224	−0.279112	+	0.960259i	$0.590040\pi$
$104$	−3.37036	−0.330491
$105$	−1.98519	−0.193735
$106$	4.48353	0.435479
$107$	2.98749	0.288812	0.144406	−	0.989519i	$-0.453873\pi$
$107$	2.98749	0.288812	0.144406	+	0.989519i	$0.453873\pi$
$108$	1.08276	0.104189
$109$	−2.94886	−0.282450	−0.141225	−	0.989978i	$-0.545104\pi$
$109$	−2.94886	−0.282450	−0.141225	+	0.989978i	$0.545104\pi$
$110$	3.20656	0.305734
$111$	−1.51933	−0.144208
$112$	3.19929	0.302305
$113$	7.95773	0.748600	0.374300	−	0.927308i	$-0.377883\pi$
$113$	7.95773	0.748600	0.374300	+	0.927308i	$0.377883\pi$
$114$	1.04559	0.0979286
$115$	19.7804	1.84453
$116$	4.63956	0.430772
$117$	−10.0001	−0.924509
$118$	6.71310	0.617991
$119$	5.99310	0.549386
$120$	0.620509	0.0566445
$121$	−10.1207	−0.920066
$122$	8.12603	0.735697
$123$	1.81821	0.163942
$124$	1.00000	0.0898027
$125$	5.79209	0.518060
$126$	9.49254	0.845662
$127$	3.39785	0.301511	0.150755	−	0.988571i	$-0.451829\pi$
$127$	3.39785	0.301511	0.150755	+	0.988571i	$0.451829\pi$
$128$	−1.00000	−0.0883883
$129$	−0.851820	−0.0749986
$130$	−11.5253	−1.01084
$131$	11.5036	1.00507	0.502537	−	0.864556i	$-0.332400\pi$
$131$	11.5036	1.00507	0.502537	+	0.864556i	$0.332400\pi$
$132$	0.170150	0.0148097
$133$	18.4351	1.59852
$134$	−10.2716	−0.887331
$135$	3.70262	0.318671
$136$	−1.87326	−0.160630
$137$	−21.0978	−1.80250	−0.901251	−	0.433297i	$-0.857350\pi$
$137$	−21.0978	−1.80250	−0.901251	+	0.433297i	$0.857350\pi$
$138$	1.04961	0.0893489
$139$	−5.52693	−0.468788	−0.234394	−	0.972142i	$-0.575311\pi$
$139$	−5.52693	−0.468788	−0.234394	+	0.972142i	$0.575311\pi$
$140$	10.9404	0.924629
$141$	1.33599	0.112511
$142$	12.2263	1.02601
$143$	−3.16037	−0.264284
$144$	−2.96707	−0.247256
$145$	15.8655	1.31756
$146$	−8.21597	−0.679959
$147$	−0.587095	−0.0484228
$148$	8.37299	0.688255
$149$	−6.78972	−0.556235	−0.278118	−	0.960547i	$-0.589710\pi$
$149$	−6.78972	−0.556235	−0.278118	+	0.960547i	$0.589710\pi$
$150$	1.21463	0.0991737
$151$	−7.41983	−0.603817	−0.301908	−	0.953337i	$-0.597624\pi$
$151$	−7.41983	−0.603817	−0.301908	+	0.953337i	$0.597624\pi$
$152$	−5.76224	−0.467379
$153$	−5.55809	−0.449345
$154$	2.99997	0.241744
$155$	3.41962	0.274670
$156$	−0.611571	−0.0489648
$157$	4.40675	0.351697	0.175848	−	0.984417i	$-0.443733\pi$
$157$	4.40675	0.351697	0.175848	+	0.984417i	$0.443733\pi$
$158$	11.8922	0.946094
$159$	0.813562	0.0645197
$160$	−3.41962	−0.270344
$161$	18.5060	1.45848
$162$	−8.70475	−0.683910
$163$	−1.91436	−0.149944	−0.0749721	−	0.997186i	$-0.523887\pi$
$163$	−1.91436	−0.149944	−0.0749721	+	0.997186i	$0.523887\pi$
$164$	−10.0201	−0.782439
$165$	0.581849	0.0452969
$166$	−10.7355	−0.833239
$167$	−23.1263	−1.78956	−0.894782	−	0.446504i	$-0.852669\pi$
$167$	−23.1263	−1.78956	−0.894782	+	0.446504i	$0.852669\pi$
$168$	0.580530	0.0447889
$169$	−1.64069	−0.126207
$170$	−6.40582	−0.491304
$171$	−17.0970	−1.30744
$172$	4.69437	0.357942
$173$	14.1024	1.07218	0.536091	−	0.844160i	$-0.319900\pi$
$173$	14.1024	1.07218	0.536091	+	0.844160i	$0.319900\pi$
$174$	0.841874	0.0638223
$175$	21.4154	1.61885
$176$	−0.937697	−0.0706815
$177$	1.21813	0.0915603
$178$	−7.48122	−0.560741
$179$	−12.2502	−0.915621	−0.457811	−	0.889050i	$-0.651366\pi$
$179$	−12.2502	−0.915621	−0.457811	+	0.889050i	$0.651366\pi$
$180$	−10.1463	−0.756257
$181$	3.83026	0.284701	0.142351	−	0.989816i	$-0.454534\pi$
$181$	3.83026	0.284701	0.142351	+	0.989816i	$0.454534\pi$
$182$	−10.7828	−0.799271
$183$	1.47452	0.108999
$184$	−5.78440	−0.426431
$185$	28.6324	2.10510
$186$	0.181456	0.0133050
$187$	−1.75655	−0.128451
$188$	−7.36262	−0.536975
$189$	3.46406	0.251974
$190$	−19.7047	−1.42953
$191$	11.6267	0.841275	0.420638	−	0.907229i	$-0.361806\pi$
$191$	11.6267	0.841275	0.420638	+	0.907229i	$0.361806\pi$
$192$	−0.181456	−0.0130954
$193$	17.2987	1.24519	0.622594	−	0.782545i	$-0.286079\pi$
$193$	17.2987	1.24519	0.622594	+	0.782545i	$0.286079\pi$
$194$	1.00000	0.0717958
$195$	−2.09134	−0.149764
$196$	3.23547	0.231105
$197$	−6.16390	−0.439160	−0.219580	−	0.975595i	$-0.570469\pi$
$197$	−6.16390	−0.439160	−0.219580	+	0.975595i	$0.570469\pi$
$198$	−2.78222	−0.197723
$199$	0.780423	0.0553227	0.0276614	−	0.999617i	$-0.491194\pi$
$199$	0.780423	0.0553227	0.0276614	+	0.999617i	$0.491194\pi$
$200$	−6.69378	−0.473322
$201$	−1.86384	−0.131465
$202$	0.582823	0.0410073
$203$	14.8433	1.04180
$204$	−0.339913	−0.0237987
$205$	−34.2649	−2.39317
$206$	5.66535	0.394724
$207$	−17.1627	−1.19289
$208$	3.37036	0.233692
$209$	−5.40323	−0.373749
$210$	1.98519	0.136991
$211$	−0.143440	−0.00987479	−0.00493740	−	0.999988i	$-0.501572\pi$
$211$	−0.143440	−0.00987479	−0.00493740	+	0.999988i	$0.501572\pi$
$212$	−4.48353	−0.307930
$213$	2.21853	0.152011
$214$	−2.98749	−0.204221
$215$	16.0530	1.09480
$216$	−1.08276	−0.0736725
$217$	3.19929	0.217182
$218$	2.94886	0.199722
$219$	−1.49084	−0.100741
$220$	−3.20656	−0.216187
$221$	6.31355	0.424695
$222$	1.51933	0.101971
$223$	18.6858	1.25129	0.625645	−	0.780108i	$-0.284836\pi$
$223$	18.6858	1.25129	0.625645	+	0.780108i	$0.284836\pi$
$224$	−3.19929	−0.213762
$225$	−19.8610	−1.32406
$226$	−7.95773	−0.529340
$227$	−0.872654	−0.0579201	−0.0289600	−	0.999581i	$-0.509220\pi$
$227$	−0.872654	−0.0579201	−0.0289600	+	0.999581i	$0.509220\pi$
$228$	−1.04559	−0.0692460
$229$	−6.98757	−0.461752	−0.230876	−	0.972983i	$-0.574159\pi$
$229$	−6.98757	−0.461752	−0.230876	+	0.972983i	$0.574159\pi$
$230$	−19.7804	−1.30428
$231$	0.544361	0.0358163
$232$	−4.63956	−0.304602
$233$	4.51769	0.295964	0.147982	−	0.988990i	$-0.452722\pi$
$233$	4.51769	0.295964	0.147982	+	0.988990i	$0.452722\pi$
$234$	10.0001	0.653727
$235$	−25.1774	−1.64239
$236$	−6.71310	−0.436986
$237$	2.15791	0.140171
$238$	−5.99310	−0.388475
$239$	−0.698701	−0.0451952	−0.0225976	−	0.999745i	$-0.507194\pi$
$239$	−0.698701	−0.0451952	−0.0225976	+	0.999745i	$0.507194\pi$
$240$	−0.620509	−0.0400537
$241$	1.87795	0.120969	0.0604846	−	0.998169i	$-0.480735\pi$
$241$	1.87795	0.120969	0.0604846	+	0.998169i	$0.480735\pi$
$242$	10.1207	0.650585
$243$	−4.82780	−0.309704
$244$	−8.12603	−0.520216
$245$	11.0641	0.706858
$246$	−1.81821	−0.115925
$247$	19.4208	1.23572
$248$	−1.00000	−0.0635001
$249$	−1.94802	−0.123451
$250$	−5.79209	−0.366324
$251$	18.6428	1.17672	0.588360	−	0.808599i	$-0.299774\pi$
$251$	18.6428	1.17672	0.588360	+	0.808599i	$0.299774\pi$
$252$	−9.49254	−0.597974
$253$	−5.42401	−0.341005
$254$	−3.39785	−0.213200
$255$	−1.16237	−0.0727906
$256$	1.00000	0.0625000
$257$	−18.7731	−1.17104	−0.585518	−	0.810659i	$-0.699109\pi$
$257$	−18.7731	−1.17104	−0.585518	+	0.810659i	$0.699109\pi$
$258$	0.851820	0.0530320
$259$	26.7876	1.66450
$260$	11.5253	0.714771
$261$	−13.7659	−0.852088
$262$	−11.5036	−0.710694
$263$	−28.4514	−1.75439	−0.877195	−	0.480135i	$-0.840588\pi$
$263$	−28.4514	−1.75439	−0.877195	+	0.480135i	$0.840588\pi$
$264$	−0.170150	−0.0104720
$265$	−15.3320	−0.941835
$266$	−18.4351	−1.13033
$267$	−1.35751	−0.0830782
$268$	10.2716	0.627438
$269$	−5.92900	−0.361498	−0.180749	−	0.983529i	$-0.557852\pi$
$269$	−5.92900	−0.361498	−0.180749	+	0.983529i	$0.557852\pi$
$270$	−3.70262	−0.225334
$271$	−30.4274	−1.84833	−0.924166	−	0.381992i	$-0.875238\pi$
$271$	−30.4274	−1.84833	−0.924166	+	0.381992i	$0.875238\pi$
$272$	1.87326	0.113583
$273$	−1.95659	−0.118418
$274$	21.0978	1.27456
$275$	−6.27674	−0.378502
$276$	−1.04961	−0.0631792
$277$	27.6648	1.66222	0.831108	−	0.556111i	$-0.187707\pi$
$277$	27.6648	1.66222	0.831108	+	0.556111i	$0.187707\pi$
$278$	5.52693	0.331483
$279$	−2.96707	−0.177634
$280$	−10.9404	−0.653811
$281$	−8.91160	−0.531621	−0.265811	−	0.964025i	$-0.585640\pi$
$281$	−8.91160	−0.531621	−0.265811	+	0.964025i	$0.585640\pi$
$282$	−1.33599	−0.0795571
$283$	22.5323	1.33940	0.669702	−	0.742630i	$-0.266422\pi$
$283$	22.5323	1.33940	0.669702	+	0.742630i	$0.266422\pi$
$284$	−12.2263	−0.725498
$285$	−3.57552	−0.211796
$286$	3.16037	0.186877
$287$	−32.0573	−1.89228
$288$	2.96707	0.174837
$289$	−13.4909	−0.793583
$290$	−15.8655	−0.931655
$291$	0.181456	0.0106371
$292$	8.21597	0.480804
$293$	29.5267	1.72497	0.862485	−	0.506083i	$-0.168907\pi$
$293$	29.5267	1.72497	0.862485	+	0.506083i	$0.168907\pi$
$294$	0.587095	0.0342401
$295$	−22.9563	−1.33656
$296$	−8.37299	−0.486670
$297$	−1.01530	−0.0589137
$298$	6.78972	0.393318
$299$	19.4955	1.12745
$300$	−1.21463	−0.0701264
$301$	15.0187	0.865662
$302$	7.41983	0.426963
$303$	0.105757	0.00607555
$304$	5.76224	0.330487
$305$	−27.7879	−1.59113
$306$	5.55809	0.317735
$307$	31.2997	1.78637	0.893184	−	0.449692i	$-0.148466\pi$
$307$	31.2997	1.78637	0.893184	+	0.449692i	$0.148466\pi$
$308$	−2.99997	−0.170939
$309$	1.02801	0.0584815
$310$	−3.41962	−0.194221
$311$	−16.4204	−0.931115	−0.465558	−	0.885018i	$-0.654146\pi$
$311$	−16.4204	−0.931115	−0.465558	+	0.885018i	$0.654146\pi$
$312$	0.611571	0.0346234
$313$	−4.54943	−0.257149	−0.128574	−	0.991700i	$-0.541040\pi$
$313$	−4.54943	−0.257149	−0.128574	+	0.991700i	$0.541040\pi$
$314$	−4.40675	−0.248687
$315$	−32.4608	−1.82896
$316$	−11.8922	−0.668989
$317$	29.0516	1.63170	0.815849	−	0.578265i	$-0.196270\pi$
$317$	29.0516	1.63170	0.815849	+	0.578265i	$0.196270\pi$
$318$	−0.813562	−0.0456223
$319$	−4.35050	−0.243581
$320$	3.41962	0.191162
$321$	−0.542098	−0.0302569
$322$	−18.5060	−1.03130
$323$	10.7942	0.600603
$324$	8.70475	0.483597
$325$	22.5604	1.25143
$326$	1.91436	0.106027
$327$	0.535088	0.0295904
$328$	10.0201	0.553268
$329$	−23.5552	−1.29864
$330$	−0.581849	−0.0320298
$331$	−14.3825	−0.790531	−0.395265	−	0.918567i	$-0.629347\pi$
$331$	−14.3825	−0.790531	−0.395265	+	0.918567i	$0.629347\pi$
$332$	10.7355	0.589189
$333$	−24.8433	−1.36140
$334$	23.1263	1.26541
$335$	35.1250	1.91908
$336$	−0.580530	−0.0316705
$337$	−1.31977	−0.0718926	−0.0359463	−	0.999354i	$-0.511445\pi$
$337$	−1.31977	−0.0718926	−0.0359463	+	0.999354i	$0.511445\pi$
$338$	1.64069	0.0892418
$339$	−1.44398	−0.0784260
$340$	6.40582	0.347405
$341$	−0.937697	−0.0507791
$342$	17.0970	0.924499
$343$	−12.0438	−0.650305
$344$	−4.69437	−0.253104
$345$	−3.58927	−0.193240
$346$	−14.1024	−0.758148
$347$	9.38016	0.503554	0.251777	−	0.967785i	$-0.418985\pi$
$347$	9.38016	0.503554	0.251777	+	0.967785i	$0.418985\pi$
$348$	−0.841874	−0.0451292
$349$	3.80634	0.203749	0.101874	−	0.994797i	$-0.467516\pi$
$349$	3.80634	0.203749	0.101874	+	0.994797i	$0.467516\pi$
$350$	−21.4154	−1.14470
$351$	3.64929	0.194785
$352$	0.937697	0.0499794
$353$	18.9666	1.00949	0.504744	−	0.863269i	$-0.331587\pi$
$353$	18.9666	1.00949	0.504744	+	0.863269i	$0.331587\pi$
$354$	−1.21813	−0.0647429
$355$	−41.8093	−2.21901
$356$	7.48122	0.396504
$357$	−1.08748	−0.0575556
$358$	12.2502	0.647442
$359$	2.91279	0.153731	0.0768657	−	0.997041i	$-0.475509\pi$
$359$	2.91279	0.153731	0.0768657	+	0.997041i	$0.475509\pi$
$360$	10.1463	0.534755
$361$	14.2034	0.747547
$362$	−3.83026	−0.201314
$363$	1.83646	0.0963893
$364$	10.7828	0.565170
$365$	28.0955	1.47059
$366$	−1.47452	−0.0770741
$367$	13.2662	0.692491	0.346245	−	0.938144i	$-0.387456\pi$
$367$	13.2662	0.692491	0.346245	+	0.938144i	$0.387456\pi$
$368$	5.78440	0.301532
$369$	29.7304	1.54770
$370$	−28.6324	−1.48853
$371$	−14.3441	−0.744710
$372$	−0.181456	−0.00940804
$373$	−20.1043	−1.04096	−0.520481	−	0.853873i	$-0.674247\pi$
$373$	−20.1043	−1.04096	−0.520481	+	0.853873i	$0.674247\pi$
$374$	1.75655	0.0908289
$375$	−1.05101	−0.0542738
$376$	7.36262	0.379698
$377$	15.6370	0.805345
$378$	−3.46406	−0.178172
$379$	−30.3787	−1.56045	−0.780224	−	0.625500i	$-0.784895\pi$
$379$	−30.3787	−1.56045	−0.780224	+	0.625500i	$0.784895\pi$
$380$	19.7047	1.01083
$381$	−0.616560	−0.0315873
$382$	−11.6267	−0.594871
$383$	−32.4935	−1.66034	−0.830170	−	0.557510i	$-0.811757\pi$
$383$	−32.4935	−1.66034	−0.830170	+	0.557510i	$0.811757\pi$
$384$	0.181456	0.00925987
$385$	−10.2587	−0.522834
$386$	−17.2987	−0.880481
$387$	−13.9285	−0.708028
$388$	−1.00000	−0.0507673
$389$	−4.36405	−0.221266	−0.110633	−	0.993861i	$-0.535288\pi$
$389$	−4.36405	−0.221266	−0.110633	+	0.993861i	$0.535288\pi$
$390$	2.09134	0.105899
$391$	10.8357	0.547983
$392$	−3.23547	−0.163416
$393$	−2.08739	−0.105295
$394$	6.16390	0.310533
$395$	−40.6668	−2.04617
$396$	2.78222	0.139812
$397$	1.58580	0.0795891	0.0397946	−	0.999208i	$-0.487330\pi$
$397$	1.58580	0.0795891	0.0397946	+	0.999208i	$0.487330\pi$
$398$	−0.780423	−0.0391191
$399$	−3.34515	−0.167467
$400$	6.69378	0.334689
$401$	39.1451	1.95481	0.977407	−	0.211366i	$-0.0677913\pi$
$401$	39.1451	1.95481	0.977407	+	0.211366i	$0.0677913\pi$
$402$	1.86384	0.0929599
$403$	3.37036	0.167889
$404$	−0.582823	−0.0289965
$405$	29.7669	1.47913
$406$	−14.8433	−0.736661
$407$	−7.85132	−0.389176
$408$	0.339913	0.0168282
$409$	6.07233	0.300257	0.150129	−	0.988666i	$-0.452031\pi$
$409$	6.07233	0.300257	0.150129	+	0.988666i	$0.452031\pi$
$410$	34.2649	1.69222
$411$	3.82831	0.188836
$412$	−5.66535	−0.279112
$413$	−21.4772	−1.05682
$414$	17.1627	0.843502
$415$	36.7114	1.80209
$416$	−3.37036	−0.165245
$417$	1.00289	0.0491119
$418$	5.40323	0.264281
$419$	15.7460	0.769244	0.384622	−	0.923074i	$-0.374332\pi$
$419$	15.7460	0.769244	0.384622	+	0.923074i	$0.374332\pi$
$420$	−1.98519	−0.0968674
$421$	11.1854	0.545144	0.272572	−	0.962135i	$-0.412126\pi$
$421$	11.1854	0.545144	0.272572	+	0.962135i	$0.412126\pi$
$422$	0.143440	0.00698253
$423$	21.8455	1.06216
$424$	4.48353	0.217740
$425$	12.5392	0.608239
$426$	−2.21853	−0.107488
$427$	−25.9976	−1.25811
$428$	2.98749	0.144406
$429$	0.573468	0.0276873
$430$	−16.0530	−0.774142
$431$	−27.2511	−1.31264	−0.656320	−	0.754483i	$-0.727888\pi$
$431$	−27.2511	−1.31264	−0.656320	+	0.754483i	$0.727888\pi$
$432$	1.08276	0.0520943
$433$	−26.1868	−1.25846	−0.629229	−	0.777220i	$-0.716629\pi$
$433$	−26.1868	−1.25846	−0.629229	+	0.777220i	$0.716629\pi$
$434$	−3.19929	−0.153571
$435$	−2.87889	−0.138032
$436$	−2.94886	−0.141225
$437$	33.3311	1.59444
$438$	1.49084	0.0712349
$439$	−34.7582	−1.65892	−0.829460	−	0.558566i	$-0.811352\pi$
$439$	−34.7582	−1.65892	−0.829460	+	0.558566i	$0.811352\pi$
$440$	3.20656	0.152867
$441$	−9.59989	−0.457138
$442$	−6.31355	−0.300305
$443$	−20.3335	−0.966073	−0.483037	−	0.875600i	$-0.660466\pi$
$443$	−20.3335	−0.966073	−0.483037	+	0.875600i	$0.660466\pi$
$444$	−1.51933	−0.0721040
$445$	25.5829	1.21275
$446$	−18.6858	−0.884796
$447$	1.23203	0.0582731
$448$	3.19929	0.151152
$449$	4.89022	0.230784	0.115392	−	0.993320i	$-0.463188\pi$
$449$	4.89022	0.230784	0.115392	+	0.993320i	$0.463188\pi$
$450$	19.8610	0.936254
$451$	9.39582	0.442432
$452$	7.95773	0.374300
$453$	1.34637	0.0632580
$454$	0.872654	0.0409557
$455$	36.8729	1.72863
$456$	1.04559	0.0489643
$457$	23.5224	1.10033	0.550167	−	0.835055i	$-0.314564\pi$
$457$	23.5224	1.10033	0.550167	+	0.835055i	$0.314564\pi$
$458$	6.98757	0.326508
$459$	2.02829	0.0946723
$460$	19.7804	0.922267
$461$	0.514289	0.0239528	0.0119764	−	0.999928i	$-0.496188\pi$
$461$	0.514289	0.0239528	0.0119764	+	0.999928i	$0.496188\pi$
$462$	−0.544361	−0.0253260
$463$	−7.23754	−0.336357	−0.168178	−	0.985757i	$-0.553788\pi$
$463$	−7.23754	−0.336357	−0.168178	+	0.985757i	$0.553788\pi$
$464$	4.63956	0.215386
$465$	−0.620509	−0.0287754
$466$	−4.51769	−0.209278
$467$	−17.7815	−0.822832	−0.411416	−	0.911448i	$-0.634966\pi$
$467$	−17.7815	−0.822832	−0.411416	+	0.911448i	$0.634966\pi$
$468$	−10.0001	−0.462255
$469$	32.8619	1.51742
$470$	25.1774	1.16135
$471$	−0.799629	−0.0368450
$472$	6.71310	0.308996
$473$	−4.40190	−0.202399
$474$	−2.15791	−0.0991161
$475$	38.5712	1.76977
$476$	5.99310	0.274693
$477$	13.3030	0.609101
$478$	0.698701	0.0319579
$479$	8.12498	0.371240	0.185620	−	0.982622i	$-0.440571\pi$
$479$	8.12498	0.371240	0.185620	+	0.982622i	$0.440571\pi$
$480$	0.620509	0.0283222
$481$	28.2200	1.28672
$482$	−1.87795	−0.0855382
$483$	−3.35801	−0.152795
$484$	−10.1207	−0.460033
$485$	−3.41962	−0.155277
$486$	4.82780	0.218994
$487$	13.1411	0.595478	0.297739	−	0.954647i	$-0.403767\pi$
$487$	13.1411	0.595478	0.297739	+	0.954647i	$0.403767\pi$
$488$	8.12603	0.367848
$489$	0.347372	0.0157087
$490$	−11.0641	−0.499824
$491$	14.0247	0.632927	0.316464	−	0.948605i	$-0.397504\pi$
$491$	14.0247	0.632927	0.316464	+	0.948605i	$0.397504\pi$
$492$	1.81821	0.0819710
$493$	8.69108	0.391427
$494$	−19.4208	−0.873783
$495$	9.51411	0.427628
$496$	1.00000	0.0449013
$497$	−39.1156	−1.75457
$498$	1.94802	0.0872930
$499$	40.5271	1.81424	0.907121	−	0.420869i	$-0.138275\pi$
$499$	40.5271	1.81424	0.907121	+	0.420869i	$0.138275\pi$
$500$	5.79209	0.259030
$501$	4.19639	0.187481
$502$	−18.6428	−0.832067
$503$	39.6647	1.76856	0.884281	−	0.466954i	$-0.154649\pi$
$503$	39.6647	1.76856	0.884281	+	0.466954i	$0.154649\pi$
$504$	9.49254	0.422831
$505$	−1.99303	−0.0886887
$506$	5.42401	0.241127
$507$	0.297713	0.0132219
$508$	3.39785	0.150755
$509$	5.24755	0.232594	0.116297	−	0.993215i	$-0.462898\pi$
$509$	5.24755	0.232594	0.116297	+	0.993215i	$0.462898\pi$
$510$	1.16237	0.0514707
$511$	26.2853	1.16279
$512$	−1.00000	−0.0441942
$513$	6.23912	0.275464
$514$	18.7731	0.828048
$515$	−19.3733	−0.853691
$516$	−0.851820	−0.0374993
$517$	6.90391	0.303634
$518$	−26.7876	−1.17698
$519$	−2.55895	−0.112326
$520$	−11.5253	−0.505419
$521$	−9.16212	−0.401400	−0.200700	−	0.979653i	$-0.564322\pi$
$521$	−9.16212	−0.401400	−0.200700	+	0.979653i	$0.564322\pi$
$522$	13.7659	0.602517
$523$	−7.64205	−0.334164	−0.167082	−	0.985943i	$-0.553434\pi$
$523$	−7.64205	−0.334164	−0.167082	+	0.985943i	$0.553434\pi$
$524$	11.5036	0.502537
$525$	−3.88594	−0.169596
$526$	28.4514	1.24054
$527$	1.87326	0.0816004
$528$	0.170150	0.00740485
$529$	10.4592	0.454749
$530$	15.3320	0.665978
$531$	19.9183	0.864380
$532$	18.4351	0.799262
$533$	−33.7713	−1.46280
$534$	1.35751	0.0587452
$535$	10.2161	0.441680
$536$	−10.2716	−0.443666
$537$	2.22286	0.0959237
$538$	5.92900	0.255617
$539$	−3.03389	−0.130679
$540$	3.70262	0.159336
$541$	22.9277	0.985739	0.492869	−	0.870103i	$-0.335948\pi$
$541$	22.9277	0.985739	0.492869	+	0.870103i	$0.335948\pi$
$542$	30.4274	1.30697
$543$	−0.695023	−0.0298263
$544$	−1.87326	−0.0803152
$545$	−10.0840	−0.431950
$546$	1.95659	0.0837345
$547$	31.7208	1.35628	0.678141	−	0.734932i	$-0.262786\pi$
$547$	31.7208	1.35628	0.678141	+	0.734932i	$0.262786\pi$
$548$	−21.0978	−0.901251
$549$	24.1105	1.02901
$550$	6.27674	0.267641
$551$	26.7342	1.13892
$552$	1.04961	0.0446744
$553$	−38.0467	−1.61791
$554$	−27.6648	−1.17536
$555$	−5.19551	−0.220537
$556$	−5.52693	−0.234394
$557$	−0.976743	−0.0413859	−0.0206930	−	0.999786i	$-0.506587\pi$
$557$	−0.976743	−0.0413859	−0.0206930	+	0.999786i	$0.506587\pi$
$558$	2.96707	0.125606
$559$	15.8217	0.669187
$560$	10.9404	0.462314
$561$	0.318735	0.0134570
$562$	8.91160	0.375913
$563$	−8.85975	−0.373394	−0.186697	−	0.982418i	$-0.559778\pi$
$563$	−8.85975	−0.373394	−0.186697	+	0.982418i	$0.559778\pi$
$564$	1.33599	0.0562553
$565$	27.2124	1.14483
$566$	−22.5323	−0.947101
$567$	27.8490	1.16955
$568$	12.2263	0.513005
$569$	25.2277	1.05760	0.528800	−	0.848746i	$-0.322642\pi$
$569$	25.2277	1.05760	0.528800	+	0.848746i	$0.322642\pi$
$570$	3.57552	0.149762
$571$	−39.9785	−1.67305	−0.836523	−	0.547931i	$-0.815415\pi$
$571$	−39.9785	−1.67305	−0.836523	+	0.547931i	$0.815415\pi$
$572$	−3.16037	−0.132142
$573$	−2.10972	−0.0881349
$574$	32.0573	1.33804
$575$	38.7195	1.61471
$576$	−2.96707	−0.123628
$577$	43.3586	1.80504	0.902521	−	0.430646i	$-0.141714\pi$
$577$	43.3586	1.80504	0.902521	+	0.430646i	$0.141714\pi$
$578$	13.4909	0.561148
$579$	−3.13895	−0.130450
$580$	15.8655	0.658779
$581$	34.3461	1.42492
$582$	−0.181456	−0.00752158
$583$	4.20419	0.174120
$584$	−8.21597	−0.339979
$585$	−34.1965	−1.41385
$586$	−29.5267	−1.21974
$587$	−24.2649	−1.00152	−0.500760	−	0.865586i	$-0.666946\pi$
$587$	−24.2649	−1.00152	−0.500760	+	0.865586i	$0.666946\pi$
$588$	−0.587095	−0.0242114
$589$	5.76224	0.237429
$590$	22.9563	0.945094
$591$	1.11847	0.0460079
$592$	8.37299	0.344128
$593$	−4.43408	−0.182086	−0.0910429	−	0.995847i	$-0.529020\pi$
$593$	−4.43408	−0.182086	−0.0910429	+	0.995847i	$0.529020\pi$
$594$	1.01530	0.0416583
$595$	20.4941	0.840176
$596$	−6.78972	−0.278118
$597$	−0.141612	−0.00579580
$598$	−19.4955	−0.797230
$599$	−46.1241	−1.88458	−0.942291	−	0.334796i	$-0.891333\pi$
$599$	−46.1241	−1.88458	−0.942291	+	0.334796i	$0.891333\pi$
$600$	1.21463	0.0495869
$601$	−42.7284	−1.74293	−0.871464	−	0.490459i	$-0.836829\pi$
$601$	−42.7284	−1.74293	−0.871464	+	0.490459i	$0.836829\pi$
$602$	−15.0187	−0.612115
$603$	−30.4766	−1.24110
$604$	−7.41983	−0.301908
$605$	−34.6090	−1.40706
$606$	−0.105757	−0.00429607
$607$	12.1111	0.491576	0.245788	−	0.969324i	$-0.420953\pi$
$607$	12.1111	0.491576	0.245788	+	0.969324i	$0.420953\pi$
$608$	−5.76224	−0.233690
$609$	−2.69340	−0.109142
$610$	27.7879	1.12510
$611$	−24.8147	−1.00389
$612$	−5.55809	−0.224673
$613$	−13.3228	−0.538105	−0.269052	−	0.963126i	$-0.586710\pi$
$613$	−13.3228	−0.538105	−0.269052	+	0.963126i	$0.586710\pi$
$614$	−31.2997	−1.26315
$615$	6.21757	0.250717
$616$	2.99997	0.120872
$617$	17.8136	0.717150	0.358575	−	0.933501i	$-0.383263\pi$
$617$	17.8136	0.717150	0.358575	+	0.933501i	$0.383263\pi$
$618$	−1.02801	−0.0413526
$619$	−34.9889	−1.40632	−0.703160	−	0.711031i	$-0.748228\pi$
$619$	−34.9889	−1.40632	−0.703160	+	0.711031i	$0.748228\pi$
$620$	3.41962	0.137335
$621$	6.26311	0.251330
$622$	16.4204	0.658398
$623$	23.9346	0.958920
$624$	−0.611571	−0.0244824
$625$	−13.6622	−0.546487
$626$	4.54943	0.181832
$627$	0.980447	0.0391553
$628$	4.40675	0.175848
$629$	15.6848	0.625392
$630$	32.4608	1.29327
$631$	−4.57679	−0.182199	−0.0910995	−	0.995842i	$-0.529038\pi$
$631$	−4.57679	−0.182199	−0.0910995	+	0.995842i	$0.529038\pi$
$632$	11.8922	0.473047
$633$	0.0260279	0.00103452
$634$	−29.0516	−1.15378
$635$	11.6194	0.461100
$636$	0.813562	0.0322598
$637$	10.9047	0.432060
$638$	4.35050	0.172238
$639$	36.2764	1.43507
$640$	−3.41962	−0.135172
$641$	3.03320	0.119804	0.0599022	−	0.998204i	$-0.480921\pi$
$641$	3.03320	0.119804	0.0599022	+	0.998204i	$0.480921\pi$
$642$	0.542098	0.0213949
$643$	16.6854	0.658006	0.329003	−	0.944329i	$-0.393287\pi$
$643$	16.6854	0.658006	0.329003	+	0.944329i	$0.393287\pi$
$644$	18.5060	0.729238
$645$	−2.91290	−0.114695
$646$	−10.7942	−0.424690
$647$	0.546843	0.0214986	0.0107493	−	0.999942i	$-0.496578\pi$
$647$	0.546843	0.0214986	0.0107493	+	0.999942i	$0.496578\pi$
$648$	−8.70475	−0.341955
$649$	6.29486	0.247095
$650$	−22.5604	−0.884893
$651$	−0.580530	−0.0227528
$652$	−1.91436	−0.0749721
$653$	−50.6418	−1.98177	−0.990883	−	0.134724i	$-0.956985\pi$
$653$	−50.6418	−1.98177	−0.990883	+	0.134724i	$0.956985\pi$
$654$	−0.535088	−0.0209236
$655$	39.3379	1.53706
$656$	−10.0201	−0.391220
$657$	−24.3774	−0.951053
$658$	23.5552	0.918277
$659$	23.1311	0.901060	0.450530	−	0.892761i	$-0.351235\pi$
$659$	23.1311	0.901060	0.450530	+	0.892761i	$0.351235\pi$
$660$	0.581849	0.0226485
$661$	22.0819	0.858885	0.429442	−	0.903094i	$-0.358710\pi$
$661$	22.0819	0.858885	0.429442	+	0.903094i	$0.358710\pi$
$662$	14.3825	0.558990
$663$	−1.14563	−0.0444925
$664$	−10.7355	−0.416619
$665$	63.0409	2.44462
$666$	24.8433	0.962657
$667$	26.8370	1.03913
$668$	−23.1263	−0.894782
$669$	−3.39064	−0.131090
$670$	−35.1250	−1.35700
$671$	7.61975	0.294157
$672$	0.580530	0.0223944
$673$	14.7375	0.568089	0.284044	−	0.958811i	$-0.408324\pi$
$673$	14.7375	0.568089	0.284044	+	0.958811i	$0.408324\pi$
$674$	1.31977	0.0508358
$675$	7.24776	0.278966
$676$	−1.64069	−0.0631035
$677$	−21.8628	−0.840257	−0.420128	−	0.907465i	$-0.638015\pi$
$677$	−21.8628	−0.840257	−0.420128	+	0.907465i	$0.638015\pi$
$678$	1.44398	0.0554555
$679$	−3.19929	−0.122778
$680$	−6.40582	−0.245652
$681$	0.158348	0.00606791
$682$	0.937697	0.0359063
$683$	22.2122	0.849925	0.424962	−	0.905211i	$-0.360287\pi$
$683$	22.2122	0.849925	0.424962	+	0.905211i	$0.360287\pi$
$684$	−17.0970	−0.653720
$685$	−72.1462	−2.75657
$686$	12.0438	0.459835
$687$	1.26793	0.0483747
$688$	4.69437	0.178971
$689$	−15.1111	−0.575687
$690$	3.58927	0.136641
$691$	1.84401	0.0701496	0.0350748	−	0.999385i	$-0.488833\pi$
$691$	1.84401	0.0701496	0.0350748	+	0.999385i	$0.488833\pi$
$692$	14.1024	0.536091
$693$	8.90112	0.338126
$694$	−9.38016	−0.356066
$695$	−18.9000	−0.716918
$696$	0.841874	0.0319112
$697$	−18.7702	−0.710974
$698$	−3.80634	−0.144072
$699$	−0.819760	−0.0310062
$700$	21.4154	0.809425
$701$	30.4456	1.14991	0.574957	−	0.818184i	$-0.305019\pi$
$701$	30.4456	1.14991	0.574957	+	0.818184i	$0.305019\pi$
$702$	−3.64929	−0.137733
$703$	48.2472	1.81968
$704$	−0.937697	−0.0353408
$705$	4.56858	0.172063
$706$	−18.9666	−0.713816
$707$	−1.86462	−0.0701263
$708$	1.21813	0.0457802
$709$	−17.3542	−0.651752	−0.325876	−	0.945413i	$-0.605659\pi$
$709$	−17.3542	−0.651752	−0.325876	+	0.945413i	$0.605659\pi$
$710$	41.8093	1.56908
$711$	35.2851	1.32329
$712$	−7.48122	−0.280370
$713$	5.78440	0.216627
$714$	1.08748	0.0406980
$715$	−10.8073	−0.404169
$716$	−12.2502	−0.457811
$717$	0.126783	0.00473481
$718$	−2.91279	−0.108704
$719$	22.6037	0.842974	0.421487	−	0.906834i	$-0.361508\pi$
$719$	22.6037	0.842974	0.421487	+	0.906834i	$0.361508\pi$
$720$	−10.1463	−0.378129
$721$	−18.1251	−0.675015
$722$	−14.2034	−0.528596
$723$	−0.340764	−0.0126732
$724$	3.83026	0.142351
$725$	31.0562	1.15340
$726$	−1.83646	−0.0681575
$727$	1.63008	0.0604564	0.0302282	−	0.999543i	$-0.490377\pi$
$727$	1.63008	0.0604564	0.0302282	+	0.999543i	$0.490377\pi$
$728$	−10.7828	−0.399636
$729$	−25.2382	−0.934749
$730$	−28.0955	−1.03986
$731$	8.79376	0.325249
$732$	1.47452	0.0544996
$733$	46.0444	1.70069	0.850345	−	0.526226i	$-0.176393\pi$
$733$	46.0444	1.70069	0.850345	+	0.526226i	$0.176393\pi$
$734$	−13.2662	−0.489665
$735$	−2.00764	−0.0740530
$736$	−5.78440	−0.213216
$737$	−9.63165	−0.354786
$738$	−29.7304	−1.09439
$739$	−0.215397	−0.00792350	−0.00396175	−	0.999992i	$-0.501261\pi$
$739$	−0.215397	−0.00792350	−0.00396175	+	0.999992i	$0.501261\pi$
$740$	28.6324	1.05255
$741$	−3.52402	−0.129458
$742$	14.3441	0.526590
$743$	12.7398	0.467377	0.233688	−	0.972312i	$-0.424920\pi$
$743$	12.7398	0.467377	0.233688	+	0.972312i	$0.424920\pi$
$744$	0.181456	0.00665249
$745$	−23.2182	−0.850650
$746$	20.1043	0.736071
$747$	−31.8531	−1.16544
$748$	−1.75655	−0.0642257
$749$	9.55786	0.349237
$750$	1.05101	0.0383774
$751$	−21.5457	−0.786213	−0.393106	−	0.919493i	$-0.628600\pi$
$751$	−21.5457	−0.786213	−0.393106	+	0.919493i	$0.628600\pi$
$752$	−7.36262	−0.268487
$753$	−3.38283	−0.123277
$754$	−15.6370	−0.569465
$755$	−25.3730	−0.923417
$756$	3.46406	0.125987
$757$	8.54047	0.310409	0.155204	−	0.987882i	$-0.450396\pi$
$757$	8.54047	0.310409	0.155204	+	0.987882i	$0.450396\pi$
$758$	30.3787	1.10340
$759$	0.984217	0.0357248
$760$	−19.7047	−0.714763
$761$	−48.4347	−1.75576	−0.877878	−	0.478884i	$-0.841042\pi$
$761$	−48.4347	−1.75576	−0.877878	+	0.478884i	$0.841042\pi$
$762$	0.616560	0.0223356
$763$	−9.43428	−0.341544
$764$	11.6267	0.420638
$765$	−19.0065	−0.687183
$766$	32.4935	1.17404
$767$	−22.6256	−0.816962
$768$	−0.181456	−0.00654772
$769$	36.1436	1.30337	0.651686	−	0.758489i	$-0.274062\pi$
$769$	36.1436	1.30337	0.651686	+	0.758489i	$0.274062\pi$
$770$	10.2587	0.369699
$771$	3.40649	0.122682
$772$	17.2987	0.622594
$773$	1.43870	0.0517466	0.0258733	−	0.999665i	$-0.491763\pi$
$773$	1.43870	0.0517466	0.0258733	+	0.999665i	$0.491763\pi$
$774$	13.9285	0.500651
$775$	6.69378	0.240448
$776$	1.00000	0.0358979
$777$	−4.86077	−0.174379
$778$	4.36405	0.156459
$779$	−57.7383	−2.06869
$780$	−2.09134	−0.0748819
$781$	11.4646	0.410235
$782$	−10.8357	−0.387482
$783$	5.02352	0.179526
$784$	3.23547	0.115553
$785$	15.0694	0.537849
$786$	2.08739	0.0744548
$787$	−45.8631	−1.63484	−0.817421	−	0.576040i	$-0.804597\pi$
$787$	−45.8631	−1.63484	−0.817421	+	0.576040i	$0.804597\pi$
$788$	−6.16390	−0.219580
$789$	5.16267	0.183796
$790$	40.6668	1.44686
$791$	25.4591	0.905222
$792$	−2.78222	−0.0988617
$793$	−27.3876	−0.972564
$794$	−1.58580	−0.0562780
$795$	2.78207	0.0986699
$796$	0.780423	0.0276614
$797$	6.39752	0.226612	0.113306	−	0.993560i	$-0.463856\pi$
$797$	6.39752	0.226612	0.113306	+	0.993560i	$0.463856\pi$
$798$	3.34515	0.118417
$799$	−13.7921	−0.487929
$800$	−6.69378	−0.236661
$801$	−22.1973	−0.784304
$802$	−39.1451	−1.38226
$803$	−7.70409	−0.271871
$804$	−1.86384	−0.0657326
$805$	63.2834	2.23045
$806$	−3.37036	−0.118716
$807$	1.07585	0.0378718
$808$	0.582823	0.0205036
$809$	−8.96811	−0.315302	−0.157651	−	0.987495i	$-0.550392\pi$
$809$	−8.96811	−0.315302	−0.157651	+	0.987495i	$0.550392\pi$
$810$	−29.7669	−1.04590
$811$	−5.67676	−0.199338	−0.0996691	−	0.995021i	$-0.531778\pi$
$811$	−5.67676	−0.199338	−0.0996691	+	0.995021i	$0.531778\pi$
$812$	14.8433	0.520898
$813$	5.52122	0.193638
$814$	7.85132	0.275189
$815$	−6.54638	−0.229310
$816$	−0.339913	−0.0118993
$817$	27.0501	0.946363
$818$	−6.07233	−0.212314
$819$	−31.9932	−1.11793
$820$	−34.2649	−1.19658
$821$	26.5874	0.927907	0.463954	−	0.885859i	$-0.346430\pi$
$821$	26.5874	0.927907	0.463954	+	0.885859i	$0.346430\pi$
$822$	−3.82831	−0.133528
$823$	−26.7336	−0.931874	−0.465937	−	0.884818i	$-0.654283\pi$
$823$	−26.7336	−0.931874	−0.465937	+	0.884818i	$0.654283\pi$
$824$	5.66535	0.197362
$825$	1.13895	0.0396531
$826$	21.4772	0.747287
$827$	−6.76362	−0.235194	−0.117597	−	0.993061i	$-0.537519\pi$
$827$	−6.76362	−0.235194	−0.117597	+	0.993061i	$0.537519\pi$
$828$	−17.1627	−0.596446
$829$	−12.3781	−0.429910	−0.214955	−	0.976624i	$-0.568960\pi$
$829$	−12.3781	−0.429910	−0.214955	+	0.976624i	$0.568960\pi$
$830$	−36.7114	−1.27427
$831$	−5.01993	−0.174140
$832$	3.37036	0.116846
$833$	6.06088	0.209997
$834$	−1.00289	−0.0347274
$835$	−79.0829	−2.73678
$836$	−5.40323	−0.186875
$837$	1.08276	0.0374256
$838$	−15.7460	−0.543938
$839$	−33.9729	−1.17287	−0.586437	−	0.809995i	$-0.699470\pi$
$839$	−33.9729	−1.17287	−0.586437	+	0.809995i	$0.699470\pi$
$840$	1.98519	0.0684956
$841$	−7.47451	−0.257742
$842$	−11.1854	−0.385475
$843$	1.61706	0.0556945
$844$	−0.143440	−0.00493740
$845$	−5.61054	−0.193008
$846$	−21.8455	−0.751062
$847$	−32.3792	−1.11256
$848$	−4.48353	−0.153965
$849$	−4.08861	−0.140321
$850$	−12.5392	−0.430090
$851$	48.4327	1.66025
$852$	2.21853	0.0760057
$853$	12.6856	0.434347	0.217174	−	0.976133i	$-0.430316\pi$
$853$	12.6856	0.434347	0.217174	+	0.976133i	$0.430316\pi$
$854$	25.9976	0.889618
$855$	−58.4652	−1.99947
$856$	−2.98749	−0.102110
$857$	34.6946	1.18514	0.592572	−	0.805517i	$-0.298112\pi$
$857$	34.6946	1.18514	0.592572	+	0.805517i	$0.298112\pi$
$858$	−0.573468	−0.0195779
$859$	−6.46151	−0.220464	−0.110232	−	0.993906i	$-0.535159\pi$
$859$	−6.46151	−0.220464	−0.110232	+	0.993906i	$0.535159\pi$
$860$	16.0530	0.547401
$861$	5.81697	0.198242
$862$	27.2511	0.928176
$863$	−8.37111	−0.284956	−0.142478	−	0.989798i	$-0.545507\pi$
$863$	−8.37111	−0.284956	−0.142478	+	0.989798i	$0.545507\pi$
$864$	−1.08276	−0.0368362
$865$	48.2247	1.63969
$866$	26.1868	0.889865
$867$	2.44800	0.0831385
$868$	3.19929	0.108591
$869$	11.1513	0.378282
$870$	2.87889	0.0976034
$871$	34.6190	1.17302
$872$	2.94886	0.0998611
$873$	2.96707	0.100420
$874$	−33.3311	−1.12744
$875$	18.5306	0.626449
$876$	−1.49084	−0.0503707
$877$	45.9198	1.55060	0.775301	−	0.631591i	$-0.217598\pi$
$877$	45.9198	1.55060	0.775301	+	0.631591i	$0.217598\pi$
$878$	34.7582	1.17303
$879$	−5.35779	−0.180714
$880$	−3.20656	−0.108093
$881$	18.8329	0.634497	0.317249	−	0.948342i	$-0.397241\pi$
$881$	18.8329	0.634497	0.317249	+	0.948342i	$0.397241\pi$
$882$	9.59989	0.323245
$883$	46.5436	1.56632	0.783158	−	0.621822i	$-0.213607\pi$
$883$	46.5436	1.56632	0.783158	+	0.621822i	$0.213607\pi$
$884$	6.31355	0.212348
$885$	4.16554	0.140023
$886$	20.3335	0.683117
$887$	44.0724	1.47981	0.739904	−	0.672713i	$-0.234871\pi$
$887$	44.0724	1.47981	0.739904	+	0.672713i	$0.234871\pi$
$888$	1.51933	0.0509853
$889$	10.8707	0.364592
$890$	−25.5829	−0.857541
$891$	−8.16241	−0.273451
$892$	18.6858	0.625645
$893$	−42.4252	−1.41971
$894$	−1.23203	−0.0412053
$895$	−41.8909	−1.40026
$896$	−3.19929	−0.106881
$897$	−3.53757	−0.118116
$898$	−4.89022	−0.163189
$899$	4.63956	0.154738
$900$	−19.8610	−0.662032
$901$	−8.39881	−0.279805
$902$	−9.39582	−0.312847
$903$	−2.72522	−0.0906897
$904$	−7.95773	−0.264670
$905$	13.0980	0.435393
$906$	−1.34637	−0.0447301
$907$	−13.4783	−0.447538	−0.223769	−	0.974642i	$-0.571836\pi$
$907$	−13.4783	−0.447538	−0.223769	+	0.974642i	$0.571836\pi$
$908$	−0.872654	−0.0289600
$909$	1.72928	0.0573566
$910$	−36.8729	−1.22233
$911$	−8.55643	−0.283487	−0.141744	−	0.989903i	$-0.545271\pi$
$911$	−8.55643	−0.283487	−0.141744	+	0.989903i	$0.545271\pi$
$912$	−1.04559	−0.0346230
$913$	−10.0667	−0.333158
$914$	−23.5224	−0.778053
$915$	5.04228	0.166693
$916$	−6.98757	−0.230876
$917$	36.8034	1.21535
$918$	−2.02829	−0.0669434
$919$	8.76381	0.289091	0.144546	−	0.989498i	$-0.453828\pi$
$919$	8.76381	0.289091	0.144546	+	0.989498i	$0.453828\pi$
$920$	−19.7804	−0.652141
$921$	−5.67951	−0.187146
$922$	−0.514289	−0.0169372
$923$	−41.2070	−1.35635
$924$	0.544361	0.0179082
$925$	56.0470	1.84281
$926$	7.23754	0.237840
$927$	16.8095	0.552097
$928$	−4.63956	−0.152301
$929$	−27.1869	−0.891973	−0.445987	−	0.895040i	$-0.647147\pi$
$929$	−27.1869	−0.891973	−0.445987	+	0.895040i	$0.647147\pi$
$930$	0.620509	0.0203473
$931$	18.6436	0.611018
$932$	4.51769	0.147982
$933$	2.97957	0.0975469
$934$	17.7815	0.581830
$935$	−6.00672	−0.196441
$936$	10.0001	0.326863
$937$	41.1114	1.34305	0.671526	−	0.740981i	$-0.265639\pi$
$937$	41.1114	1.34305	0.671526	+	0.740981i	$0.265639\pi$
$938$	−32.8619	−1.07298
$939$	0.825520	0.0269398
$940$	−25.1774	−0.821195
$941$	−31.6019	−1.03019	−0.515096	−	0.857132i	$-0.672244\pi$
$941$	−31.6019	−1.03019	−0.515096	+	0.857132i	$0.672244\pi$
$942$	0.799629	0.0260533
$943$	−57.9603	−1.88745
$944$	−6.71310	−0.218493
$945$	11.8458	0.385343
$946$	4.40190	0.143118
$947$	−6.32069	−0.205395	−0.102697	−	0.994713i	$-0.532747\pi$
$947$	−6.32069	−0.205395	−0.102697	+	0.994713i	$0.532747\pi$
$948$	2.15791	0.0700857
$949$	27.6908	0.898880
$950$	−38.5712	−1.25141
$951$	−5.27157	−0.170942
$952$	−5.99310	−0.194237
$953$	28.1602	0.912200	0.456100	−	0.889929i	$-0.349246\pi$
$953$	28.1602	0.912200	0.456100	+	0.889929i	$0.349246\pi$
$954$	−13.3030	−0.430700
$955$	39.7587	1.28656
$956$	−0.698701	−0.0225976
$957$	0.789422	0.0255184
$958$	−8.12498	−0.262506
$959$	−67.4979	−2.17962
$960$	−0.620509	−0.0200268
$961$	1.00000	0.0322581
$962$	−28.2200	−0.909848
$963$	−8.86411	−0.285642
$964$	1.87795	0.0604846
$965$	59.1549	1.90426
$966$	3.35801	0.108042
$967$	6.75713	0.217295	0.108647	−	0.994080i	$-0.465348\pi$
$967$	6.75713	0.217295	0.108647	+	0.994080i	$0.465348\pi$
$968$	10.1207	0.325292
$969$	−1.95866	−0.0629212
$970$	3.41962	0.109797
$971$	35.7324	1.14671	0.573354	−	0.819307i	$-0.305642\pi$
$971$	35.7324	1.14671	0.573354	+	0.819307i	$0.305642\pi$
$972$	−4.82780	−0.154852
$973$	−17.6823	−0.566868
$974$	−13.1411	−0.421067
$975$	−4.09372	−0.131104
$976$	−8.12603	−0.260108
$977$	−60.0955	−1.92262	−0.961312	−	0.275461i	$-0.911170\pi$
$977$	−60.0955	−1.92262	−0.961312	+	0.275461i	$0.911170\pi$
$978$	−0.347372	−0.0111077
$979$	−7.01511	−0.224204
$980$	11.0641	0.353429
$981$	8.74949	0.279350
$982$	−14.0247	−0.447547
$983$	−26.1276	−0.833341	−0.416671	−	0.909057i	$-0.636803\pi$
$983$	−26.1276	−0.833341	−0.416671	+	0.909057i	$0.636803\pi$
$984$	−1.81821	−0.0579623
$985$	−21.0782	−0.671607
$986$	−8.69108	−0.276780
$987$	4.27422	0.136050
$988$	19.4208	0.617858
$989$	27.1541	0.863450
$990$	−9.51411	−0.302378
$991$	36.3621	1.15508	0.577540	−	0.816362i	$-0.304013\pi$
$991$	36.3621	1.15508	0.577540	+	0.816362i	$0.304013\pi$
$992$	−1.00000	−0.0317500
$993$	2.60978	0.0828188
$994$	39.1156	1.24067
$995$	2.66875	0.0846050
$996$	−1.94802	−0.0617255
$997$	17.5622	0.556200	0.278100	−	0.960552i	$-0.410295\pi$
$997$	17.5622	0.556200	0.278100	+	0.960552i	$0.410295\pi$
$998$	−40.5271	−1.28286
$999$	9.06593	0.286833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.19	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.19	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.181456 q^{3} +1.00000 q^{4} +3.41962 q^{5} +0.181456 q^{6} +3.19929 q^{7} -1.00000 q^{8} -2.96707 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.181456 q^{3} +1.00000 q^{4} +3.41962 q^{5} +0.181456 q^{6} +3.19929 q^{7} -1.00000 q^{8} -2.96707 q^{9} -3.41962 q^{10} -0.937697 q^{11} -0.181456 q^{12} +3.37036 q^{13} -3.19929 q^{14} -0.620509 q^{15} +1.00000 q^{16} +1.87326 q^{17} +2.96707 q^{18} +5.76224 q^{19} +3.41962 q^{20} -0.580530 q^{21} +0.937697 q^{22} +5.78440 q^{23} +0.181456 q^{24} +6.69378 q^{25} -3.37036 q^{26} +1.08276 q^{27} +3.19929 q^{28} +4.63956 q^{29} +0.620509 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.170150 q^{33} -1.87326 q^{34} +10.9404 q^{35} -2.96707 q^{36} +8.37299 q^{37} -5.76224 q^{38} -0.611571 q^{39} -3.41962 q^{40} -10.0201 q^{41} +0.580530 q^{42} +4.69437 q^{43} -0.937697 q^{44} -10.1463 q^{45} -5.78440 q^{46} -7.36262 q^{47} -0.181456 q^{48} +3.23547 q^{49} -6.69378 q^{50} -0.339913 q^{51} +3.37036 q^{52} -4.48353 q^{53} -1.08276 q^{54} -3.20656 q^{55} -3.19929 q^{56} -1.04559 q^{57} -4.63956 q^{58} -6.71310 q^{59} -0.620509 q^{60} -8.12603 q^{61} -1.00000 q^{62} -9.49254 q^{63} +1.00000 q^{64} +11.5253 q^{65} -0.170150 q^{66} +10.2716 q^{67} +1.87326 q^{68} -1.04961 q^{69} -10.9404 q^{70} -12.2263 q^{71} +2.96707 q^{72} +8.21597 q^{73} -8.37299 q^{74} -1.21463 q^{75} +5.76224 q^{76} -2.99997 q^{77} +0.611571 q^{78} -11.8922 q^{79} +3.41962 q^{80} +8.70475 q^{81} +10.0201 q^{82} +10.7355 q^{83} -0.580530 q^{84} +6.40582 q^{85} -4.69437 q^{86} -0.841874 q^{87} +0.937697 q^{88} +7.48122 q^{89} +10.1463 q^{90} +10.7828 q^{91} +5.78440 q^{92} -0.181456 q^{93} +7.36262 q^{94} +19.7047 q^{95} +0.181456 q^{96} -1.00000 q^{97} -3.23547 q^{98} +2.78222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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